Chapter 7. Logic and Critical Reasoning
Logic is the study of correct reasoning. An argument consists of premises offered as support for a conclusion [12][13].
Validity and soundness. A deductive argument is valid if the conclusion must be true whenever the premises are true; it is sound if it is valid and its premises are true. An inductive argument gives probable support and is judged strong or weak [12][13].
Categorical (syllogistic) logic. Four standard statement forms: A (All S are P), E (No S are P), I (Some S are P), O (Some S are not P). A syllogism has two premises and a conclusion with three terms. Example: All humans are mortal; all Greeks are humans; therefore all Greeks are mortal. Venn diagrams test validity [12].
Propositional logic. Connectives are not (¬), and (∧), or (∨), if–then (→) and if and only if (↔).
| P | Q | P ∧ Q | P ∨ Q | P → Q |
|---|---|---|---|---|
| T | T | T | T | T |
| T | F | F | T | F |
| F | T | F | T | T |
| F | F | F | F | T |
Valid argument forms. Modus ponens: P → Q; P; therefore Q. Modus tollens: P → Q; not Q; therefore not P. Hypothetical syllogism: P → Q; Q → R; therefore P → R. Invalid forms include affirming the consequent (P → Q; Q; therefore P) and denying the antecedent [13].
De Morgan’s laws: ¬(P ∧ Q) is equivalent to ¬P ∨ ¬Q; ¬(P ∨ Q) is equivalent to ¬P ∧ ¬Q.
Informal fallacies. Ad hominem, straw man, false dilemma, slippery slope, appeal to authority, circular reasoning, hasty generalization, equivocation and appeal to emotion [12][13].
Induction and scientific reasoning. Scientific theories make testable predictions; Popper argued that good theories are falsifiable [14]. Beware of correlation confused with causation.
Definitions and language. Definitions clarify terms; ambiguity and vagueness can cause confusion.
Review: Is this argument valid? “If it rains, the ground is wet. The ground is wet. Therefore it rained.” (Answer: no; it affirms the consequent, because the ground could be wet for other reasons.)